If the nth term of a progression be a linear expression in n, then prove that this progression is an AP - Mathematics

Advertisements
Advertisements
Sum

If the nth term of a progression be a linear expression in n, then prove that this progression is an AP

Advertisements

Solution

Let the nth term of a given progression be given by Tn = an + b, where a and b are constants.

Then, Tn-1 = a(n – 1) + b = [(an + b) – a]

∴ (Tn – Tn-1 ) = (an + b) – [(an + b) – a] = a,

which is a constant.

Hence, the given progression is an AP

  Is there an error in this question or solution?

RELATED QUESTIONS

A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?


If m times mth term of an A.P. is equal to n times its nth term, then show that (m + n)th term of the A.P. is zero.


If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13th term is zero


State whether the following sequence is an Arithmetic Progression or not:
3, 6, 12, 24,......


Write the next two terms of A.P. whose first term is 3 and the common difference is 4.


Show that the sequence defined by an = 5n −7 is an A.P, find its common difference.


Find Is 68 a term of the A.P. 7, 10, 13, ...?


Find the sum of all multiples of 7 lying between 500 and 900.


The first term and the common difference of an A. P. is 10,000 and
2000 resectively. Find the sum of first 12 terms of the A.P.


Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

12, 32, 52, 72, ...


Find the common difference of the A.P. and write the next two terms  51, 59, 67, 75, ..


Define an arithmetic progression.

 

Check whether the following sequence is in A.P.

a – 3, a – 5, a – 7, …


Check whether the following sequence is in A.P.

`1/2, 1/3, 1/4, 1/5, ...`


Check whether the following sequence is in A.P.

1, –1, 1, –1, 1, –1, …


First term a and common difference d are given below. Find the corresponding A.P.

a = `3/4`, d = `1/2`


If nine times ninth term is equal to the fifteen times fifteenth term, show that six times twenty fourth term is zero


The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term


In the winter season let us take the temperature of Ooty from Monday to Friday to be in A.P. The sum of temperatures from Monday to Wednesday is 0°C and the sum of the temperatures from Wednesday to Friday is 18°C. Find the temperature on each of the five days.


If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is


If the sequence t1, t2, t3 … is in A.P. then the sequence t6, t12, t18 … is


Find the 12th term from the last term of the A.P – 2, – 4, – 6, … – 100


Choose the correct alternative answer for the following sub question

For an A.P. 5, 12, 19, 26, … a = ?


Decide whether the given sequence 2, 4, 6, 8,… is an A.P.


Find a and d for an A.P., 1, 4, 7, 10,.........


Find common difference of an A.P., 0.9, 0.6, 0.3 ......


Which term of following A.P. is −940.

50, 40, 30, 20 ........

Activity :- Here a = `square`, d = `square`, tn = −940

According to formula, tn = a + (n − 1)d

−940 = `square`

n = `square`


In an A.P., a = 10 and d = −3 then find its first four terms


1, 7, 13, 19 ...... find 18th term of this A.P.


Merry got a job with salary ₹ 15000 per month. If her salary increases by ₹ 100 per month, how much would be her salary after 20 months?


Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......


Which of the following form an AP? Justify your answer.

11, 22, 33,...


Verify that the following is an AP, and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1),...


For an A.P., if a = 7 and d = 2.5 then t12 = ?


For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.


Statement A (Assertion): `-5, (-5)/2, 0, 5/2`, .... is in Arithmetic Progression.

Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.


Share
Notifications



      Forgot password?
Use app×